This activity is targeted towards high school students who
have taken or are taking pre-calculus.

Goals:

Through this activity, students will learn the basic principles
of magnetism and how they apply to the Sun.

Magnetism

Why study magnetism?

Magnetism is important in the study of the Sun, since it plays
a key role in the dynamics of its surface. It is in part responsible for
eruptions called coronal mass ejections
that release high amounts of energy into space. If the radiation from these
eruptions reach Earth, they can damage satellites, interrupt electronic
communications, and even bring down electrical power grids. Like meteorologists
who study thermodynamics in an attempt to predict the weather, solar physicists
study magnetism on the Sun in hopes of understanding the "space weather"
created by the Sun.

What is magnetism?

Magnetism is phenomenon that arises out of the movement
of electric charge, a fundamental property of matter. It creates a
magnetic force, a "push" or "pull", on objects with moving electric charge.

Magnetism can also be demonstrated with a pair of magnets. Although
currents, or a moving flow of electrons, are not present within them, magnets
do in fact have moving electric charge at the atomic level. The electrons
within the magnets are thought to spin in the same direction, resulting
in a magnetic field. As a result of this self created field, each magnet
has a polarity, or two poles, north and south. When a pole of a magnet
is brought to the same pole of the other, the two magnets repel. When the
poles are different, the magnets attract. As a pair of magnets can show,
the movement of electric charge is the driving force of magnetism, which
we will continue to study in further depth.

Magnetic fields

One way to describe magnetism is through magnetic fields.
A magnetic field defines the magnetic force, the "push" or "pull," felt
by a particle independent of its charge and velocity (the speed and direction
of the particle) due to the presence of other moving charges. The stronger
the field, the stronger the magnetic force felt by the particle. Likewise,
the weaker the field, the weaker the magnetic force.

Magnetic fields can be visualized using magnetic field lines.
These lines are curves where:

At every given point the tangent (the line that intersects the curve only
at the given point for an infinitesimal distance) is in the same direction
as the magnetic field. If one were to place a compass in a magnetic field,
the needle would point tangent to the magnetic field line.

The magnetic field magnitude is proportional to the density of the lines.
The closer together the field lines, the stronger the magnetic field. The
more spread out they are, the weaker the magnetic field.

Magnetic field lines on the Sun

The image above is from a computer
simulation of how the Sun's corona, or outer atmosphere, is heated
by its "magnetic carpet." The loops that extend into the corona are magnetic
field lines that join the north and south poles in the "magnetic carpet".

Observing magnetic fields experiment: The magnetic fields of a magnet
can be indirectly observed using iron filings.

Equipment:

bar magnets
a piece of cardboard much larger than a bar magnet
iron filings
a table

Assembly:

Place a bar magnet on the table

Place the cardboard on top of the magnet.

Scatter the iron filings evenly over the cardboard.

Procedure:

Observe the iron filings. Are they pointed in any certain direction? Where
do the filings concentrate, near regions of weaker or stronger magnetic
field?

Using the pattern formed by the iron filings as a guide, draw a magnetic
field line diagram for the given magnet.

In your magnetic field line diagram, make note of where the field lines
are spread apart or concentrated. Using a pair of magnets, determine which
parts of a magnet are stronger or weaker. Establish a relationship between
the magnetic forces you felt using the pair of magnets and the concentration
of field lines in your diagram.

What's Going On?

The magnetic field created by the bar magnet induces a magnetic
field in the iron filings. The iron filings become little magnets. Because
the iron filings are rod-shaped, they have a tendency to form their poles
in a lengthwise direction. As a result, they point in the same direction
of applied magnetic field of the bar magnet, just as a compass needle would
do when brought next to a magnet.

Magnetograms

Magnetic
fields can also be visualized as magnetograms,
which are used to make observations of the Sun. Magnetograms are visual
representations of the polarity and the strength of magnetic fields that
point directly away or towards the observer. Black regions have the strongest
southward field (the field points away from the observer and into the Sun),
and white regions have the strongest northward field (the field points
towards the observer and away from the Sun). Gray areas have little or
no magnetic field. One such instrument that generates magnetograms from
its observations is the Michelson Doppler Imager (MDI) aboard the SOHO
satellite. Daily
magnetograms from this instrument are available.

Magnetic force

Using the idea of fields that we explored in the previous section,
the magnetic force exerted on a given particle can be expressed as follows
in SI units:

Fmag = qvBsinq (1)

Where q is the amount of charge, v the velocity of the particle, B the
magnetic field, and q the angle formed between
the velocity and magnetic field directions.

If you are familiar with vectors and vector math, the magnetic force
equation can be expressed in a more elegant form in SI units as:

Fmag = qv x B

In circuits, electrons, which have a negative charge, are moving through
the wires. This flow of electrons, a unit charge per unit second, is called
current.
As a result of this current, magnetic fields are created around wires.
Hans Christian Oersted (1777-1851) stumbled upon this phenomenon after
a lecture that he had given. He observed that if a compass was placed parallel
to a wire with flowing current, the compass needle would deflect. Perhaps
the reason why magnetic force was not detected in wires until Oersted is
because of the large amount of current needed to create a measurable magnetic
force. The relative weakness of magnetic force, compared to electric force
that arises out of the presence of electric charge, can be seen in the
next experiment with a wire coil and magnet.

Force between a wire coil and magnet: The fact that moving charges
create magnetic force can be seen in a wire coil with current flowing through
it and a magnet.

Equipment:

Thick magnet wire for the coil (around #20 gauge)
Thin magnet wire that is light and flexible (around #36 gauge)
A Magnet
Power supply
Stands (to hold the coil)
Thread (to suspend the coil from the stand)
Wires with alligator clips
Graph paper
A flat surface such as a textbook (should be able to hold the graph
paper vertical)

Assembly:

Wrap the thick magnet wire around a cylindrical object such as a pen and
count the number of turns made. Make thirty to forty turns. Be sure that
the wire is wrapped evenly. Record the number of turns.

Trim the ends of the wire so that they are about the same length. Burn
off the enamel on the ends by passing them through a lighted match. Another
way to remove the enamel is by scrapping it off using a pair of scissors
or pliers.

Carefully remove the coil from the cylindrical object so that its shape
is preserved.

Tie one end of the string around the middle of the coil so that when suspended,
it hangs horizontally. Tie the other end to the stand, suspending the coil.

Remove the enamel on the ends of two thin magnet wires in the same way
that enamel was removed for the thick wire. Connect an end of a thin wire
to one end of the coil. Do the same to the other coil end with the other
thin wire. This allows the coil swing easily without being restricted by
heavy wires.

Connect a wire with alligator clips to one thin wire. Do the same with
the other thin wire. Make sure that the thin wire is long enough, so that
the metal of the alligator clips does not interfere with the magnet when
it is brought up to the coil.

Connect the other ends of the wires with alligator clips to the power supply,
forming a circuit.

Tape the graph paper to the flat surface and stand the surface up behind
the coil. With a pencil, place a mark on the graph paper directly behind
the right side of the coil. This allows us to measure the distance the
coil has moved when a magnet is placed next to it.

Procedure:

Turn on the power supply. Turn the current up to one ampere or the highest
setting if one ampere cannot be reached. A current will flow through the
coil, resulting in a magnetic field.

Bring a magnet close to the right end of the coil. Does the coil repel
or attract?

Orient the magnet so that the coil is attracted to the magnet. Being careful
to see that the thin wires are not pulling the coil, pull the coil to the
right from its initial position using the magnet. Place a mark on the graph
paper at the location of the right side of coil where the coil falls away.
Also write the amount of current being provided by the power supply next
the mark.

Decrease the amount of current provided by the power supply. Repeat steps
two and three. Continue decreasing the current until a satisfactory number
of measurements are made.

If you have extra magnet wire, make another coil, this time with a fewer
number of turns and conduct the same experiment (steps one through four)
as before.

What's Going On?

According to Equation 1, Fmag = qvBsinq,
magnetic force arises out of the movement of electrons in the coil (the
qv part) and the application of a magnetic field supplied by the magnet
(the B part). The movement of charge through the coil, which also gives
rise to the coil's own magnetic field, and the magnetic field of the magnet
is why a force is felt between the two object. As for the need to coil
the wire, coiling allows more charge to flow through the wire in a smaller
volume, thus increasing magnetic force. If we were to use a straight wire,
a magnetic force would still be present, but it would be so slight that
it could not be observed easily. The coil falls away at a certain point
because gravity is pulling down on it, and the magnetic force between the
coil and magnet is great enough to overcome the opposing gravitational
force.

Calculations:

Using the data obtained from the experiment, show that the
magnetic force is directly proportional to the amount of current provided
(which is related to qv in Equation 1). Also, if more than one coil was
made, establish a relationship between the number of coils and the strength
of the magnetic force.

Applying this idea to the Sun, we see that magnetic fields and force arise
out of the movement of charges through its highly conductive plasma, just
as magnetic fields and force arose out of the movement of current through
the coil.

Stored energy in magnetic fields

The final aspect of magnetism that is necessary to have a basic
understanding of the dynamics on the surface of the Sun is the idea that
magnetic fields can store energy. The energy stored in a magnetic field
is essentially the total amount of work required to assemble a system of
moving charges. Stored energy in magnetic fields can be illustrated in
the following experiment with a pair of magnets.

Magnet Acrobatics:

Equipment:

Two magnets

Procedure:

Place a magnet on the table and hold it in place with one hand.

Orient the other magnet above the one on the table such that each pole
faces the same pole on the other magnet.

Bring the top magnet down onto the other one on the table. The magnets
should repel each other as you do this. Hold the stacked magnets together.

Let go of the magnets, being sure to move your hands out of the way. The
magnets will perform their acrobatics.

What's Going On?

When the two magnets are brought together, a force must be
exerted for a given distance, i.e. work is being done to bring these two
magnets together. Energy in the form of moving magnets is released when
the one lets go of them. This release of energy causes them to jump.

Magnetism on the Sun

Combining our understanding of the basic features of magnetism,
specifically magnetic fields, magnetic force, and the storage of energy
in magnetic fields, we can now focus on magnetism particular to the Sun.

Magnetic reconnection

One important aspect of magnetism on the Sun is magnetic
reconnection, which can be better understood if we first
examine what plasma is. Plasma
is a state of matter occurring at high temperatures where electrons are
not bound to the nucleus. As a result, ions and electrons are free to move
about the material. The free movement of charges makes plasma highly conductive,
thereby causing magnetic field lines to be "frozen" into the plasma.

In reconnection, fluid motions in plasma bring together two "frozen"
and oppositely directed magnetic field lines. These field lines then reconnect
into a lower energy state. As we found out in the Magnet Acrobatics
activity,
magnetic fields can store energy. Energy is stored in reconnection when
the "frozen" field lines become distorted as a result of fluid motion.
Reconnection reduces the amount of distortion, which in turn causes energy
to be released. This can be illustrated in the following activity with
rubber bands.

Reconnecting Rubber Bands - Since magnetic reconnection occurs
in plasmas, which cannot be feasibly produced in a high school lab, we
will have to be content with an activity using rubber bands to model magnetic
reconnection. This activity requires two people.

Equipment:

A flat rubber band
Two binder clips
A marker
A pair of scissors

Procedure:

Have your partner stretch out the rubber band into a rectangle using the
index finger and thumb of both hands as corners.

Use a marker to draw four arrows on each side of the rubber band rectangle.
The arrows should point in the direction of a closed path traced along
the rubber band. The rubber band now represents magnetic field lines.

Choose two opposing sides of the rectangle and pinch them together. This
is simulating the distortion of magnetic fields that occurs before reconnection.

Hold the two opposing sides together with both binder clips.

Take a pair of scissors and cut the two "magnetic field lines" between
the binder clips. This is simulating reconnection of the field lines.

Note that energy from the rubber bands is released, which also happens
during magnetic reconnection.

Magnetic reconnection is important to solar physicists since they think
that it in part is the cause of flares and coronal mass ejections (CMEs).
It is also thought to be a possible heat source for the corona, which is
unexpectedly hotter than the surface layers below it.

Sunspots

Magnetism
is also responsible for the formation of sunspots.
Sunspots are small areas on the Sun that appear dark because of their relative
low temperature. This low temperature is thought to be caused by magnetic
fields. The magnetic field inhibits convection, or the distribution of
heat, resulting in a cool sunspot (Tayler
29).

Faculae
(or photospheric faculae) are bright areas above the photosphere that appear
near sunspots. Although they occur everywhere on the Sun, faculae can only
be seen on the limb, or edge of the Sun. This is a result of limb darkening
and the different temperatures of the faculae. Limb darkening occurs because
only the shallow layers of the Sun that are cooler and less bright can
be seen at the limb. Consequently, the limb appears darker than the rest
of the Sun. Likewise, only the upper or shallow layers of the faculae can
be seen at the limb. Since the upper layers of the faculae are several
hundred degrees hotter than the photosphere (whereas its lower layers are
cooler) and consequently brighter than the rest of the darkened limb, the
faculae is visible.

Flares
are eruptions of particles and radiation on the surface of the Sun. They
are the result of a buildup in activity around sunspots. Lasting up to
an hour, they release massive amounts of energy equivalent to a billion
megatons of dynamite (Hathaway par.1). The
energy that they release is thought to be from
magnetic reconnnection.

Prominences
are arch-like structures in the corona and are seen at the limb of the
Sun. They are called filaments when they are projected onto the
disk of the Sun. These structures are supported by long lasting magnetic
field formations in quiescent prominences. Active prominences occur over
sunspots, whereas quiescent prominences appear where there are no sunspots
or with decaying sunspot groups.

Coronal mass ejections

One of the most significant consequences of magnetism is the coronal
mass ejection (CME), a large scale and sudden expulsion of magnetized
plasma from the Sun's corona, or outer atmosphere (Wagner
267). CMEs are so large that they can occupy as much as a quarter of
the solar limb. Despite their size, CMEs were not discovered until the
1970s, in part because the Earth's atmosphere prevented instruments from
detecting their presence and the erroneous attribution of geomagnetic storms
primarily to solar flares. CMEs can send so many charged particles at high
speeds to the Earth that they penetrate the magnetosphere, a cavity
created by the Earth's own magnetic field that deflects particles from
the solar wind. These geomagnetic storms caused by CMEs can disrupt communications
& navigation systems, satellites and power grids. Like flares, CMEs
derive their energy from magnetic fields. The twisting and distortion of
magnetic field lines stores energy in the field which is later released
when a CME forms.

The flare "myth"

Before modern observations proved otherwise, the majority of
scientists believed that the geomagnetic storms experienced on Earth were
a result of solar flares. As a result, they based
their theories on a strong causal relationship between flares and geomagnetic
stores. However, starting with the discovery of coronal mass eruptions
(which are called coronal mass ejections today) in the spacecraft observations
of
OSO-7 and Skylab, it is clear that this
relationship is wrong (Kahler
114, Gosling
par.3). Coronal mass ejections rather than flares are the causes of
energy release and geomagnetic storms. Unlike what was also previously
thought, flares are not even required for coronal mass ejections to take
place.